The elastic response of BaTiO$_3$ single crystals during electric field cycling at room temperature has been studied using in-situ Resonant Ultrasound Spectroscopy (RUS), which allows monitoring of both the elastic and anelastic changes caused by ferroelectric polarization switching. We find that the first ferroelectric switching of a virgin single crystal is dominated by ferroelastic 90{deg} switching. In subsequent ferroelectric switching, ferroelastic switching is reduced by domain pinning and by the predominance of 180{deg} ferroelectric domains, as confirmed by polarized light microscopy. RUS under in-situ electric field therefore demonstrates to be an effective technique for the investigation of electromechanical coupling in ferroelectrics.